But in your hearts revere Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect. 1 Peter 3:15

There are many problems with this gospel, the first of which is that the gospel has no direct claim of ownership.

To clarify, the book is written in the first person with the narrator being Peter, but no claim to authorship is made by Peter. Because the book has been written in this style, it is generally attributed to by Peter.

Additionally, church historian Eusebius (263-339 AD) warned about a false gospel claimed to be written by Peter.

He said that:

1. One epistle of Peter, that called the first, is acknowledged as genuine. And this the ancient elders used freely in their own writings as an undisputed work. But we have learned that his extant second Epistle does not belong to the canon; yet, as it has appeared profitable to many, it has been used with the other Scriptures.2. The so-called Acts of Peter, however, and the Gospel which bears his name, and the Preaching and the Apocalypse, as they are called, we know have not been universally accepted, because no ecclesiastical writer, ancient or modern, has made use of testimonies drawn from them.3. But in the course of my history I shall be careful to show, in addition to the official succession, what ecclesiastical writers have from time to time made use of any of the disputed works, and what they have said in regard to the canonical and accepted writings, as well as in regard to those which are not of this class.4. Such are the writings that bear the name of Peter, only one of which I know to be genuine and acknowledged by the ancient elders.